how do you find the perpendicular distance between a line segment and a point? (photo attached) i’m stuck
Answers
Answer:
Exact Distance = [tex]\frac{4\sqrt{10}}{5}[/tex]
Approximate Distance = 2.529822
============================================
Explanation:
This process is quite involved if you don't know the shortcut formula. I'll go over the long method first, and then show the shortcut in the next section.
First we'll need the equation of the line through points O and M. Use of the slope formula will show line OM has slope -1/3, which you are correct in stating.
Then use point slope form to determine the equation of line OM is y = (-1/3)x+11/3. This converts to the standard form x+3y = 11.
For anything in the form Ax+By = C, the equation perpendicular to this is of the form Bx-Ay = D. The A,B coefficients swap, and one item is negated. This helps form the negative reciprocal slope needed for the perpendicular line.
Compare x+3y = 11 to Ax+By = C. We see that A = 1 and B = 3.
So Bx-Ay = D turns into 3x-y = D. Then plug in the coordinates of H(-3,2) and compute to get
3x-y = 3(-3)-2 = -9-2 = -11. So D = -11
The equation 3x-y = D turns into 3x-y = -11 which is the equation of the line through point H and this line is perpendicular to line OM.
At this point, we have this system of equations
x+3y = 11
3x-y = -11
Solve that system however you wish. Substitution may be the best choice. Doing so leads to the intersection point (-2.2, 4.4)
The last step is to apply the distance formula between the points H(-3,2) and the intersection point (-2.2, 4.4)
The distance you should get is [tex]\frac{4\sqrt{10}}{5} \approx 2.529822[/tex]
I'm skipping steps because listing everything out would take up way too much space in my opinion.
--------------------------------------------------------
The first section goes over a fairly lengthy process of finding the perpendicular distance. Luckily, there's a shortcut.
Consider an equation of the form Ax+By=C, aka standard form. Now consider a point P located at (m,n) that is not on the line Ax+By = C. We can find the distance from P to the line using this formula below
[tex]d = \frac{|Am+Bn-C|}{\sqrt{A^2+B^2}}[/tex]
In this case, A = 1, B = 3 and C = 11 found back in the previous section. So you'll still need to calculate the equation of line OM.
Also, we'll use (m,n) = (-3,2) which are the coordinates of point H
From here it's a fairly straightforward computation
[tex]d = \frac{|Am+Bn-C|}{\sqrt{A^2+B^2}}\\\\d = \frac{|1*(-3)+3*2-11|}{\sqrt{(1)^2+(3)^2}}\\\\d = \frac{|-8|}{\sqrt{1+9}}\\\\d = \frac{8}{\sqrt{10}}\\\\[/tex]
Optionally we can rationalize the denominator like so
[tex]d = \frac{8}{\sqrt{10}}\\\\d = \frac{8\sqrt{10}}{\sqrt{10}\sqrt{10}}\\\\d = \frac{8\sqrt{10}}{\sqrt{10*10}}\\\\d = \frac{8\sqrt{10}}{\sqrt{100}}\\\\d = \frac{8\sqrt{10}}{10}\\\\d = \frac{2*4\sqrt{10}}{2*5}\\\\d = \frac{4\sqrt{10}}{5}\\\\d \approx 2.529822\\\\[/tex]
There are different ways to write down the answer, but they all represent the same number.
Related Questions
Sally examined the three triangles pictured below. What is a possible conjecture
Answers
Answer:
where are the triangles
A baseball bat factory produces 24,000 bats per day and uses 50 boxes for packing the bats. If the number of boxes needed for packing is proportional to the number of bats produced, how many boxes would be needed on a day when 36,000 bats are produced?
Answers
Answer:
Total boxes= 75
Step-by-step explanation:
Giving the following information:
A baseball bat factory produces 24,000 bats per day and uses 50 boxes for packing the bats.
First, we need to determine the number of bats that fits into a box:
Bats per box= 24,000 / 50
Barts per box= 480
Now, the number of boxes for 36,000 bats:
Total boxes= total bats / bats per box
Total boxes= 36,000/480
Total boxes= 75
Answer:75
Step-by-step explanation:
Bats 24000/50
Box 480
For each shape, write an expression for the missing length. Area =9x -6 , length=3x-2, breath =?
Answers
the breadth of the rectangle is 3
A rectangle is composed of two sides: length (L) and width (W). The length of a rectangle is the longest side, whereas the width is the shortest side. The width of a rectangle is sometimes referred to as the breadth (b).
Area =9x -6 ,
length=3x-2,
breath =?
Therefore, the area of a rectangle formula states that:
Area of rectangle = Length x Width
A = L * W, where A is the area, L is the length, W is the width or breadth.
now put the given value in the formula
9x-6 = (3x-2 )*W
3( 3x -2) / (3x-2) = W
W =3
Hence , the breadth of the rectangle is 3
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Twice a number added to another number is 15. The sum of the two numbers is 11. Find the numbers. Write the numbers from least to greatest
Answers
Answer:
(6,8)
I know because I did it coool
Please help :( 20 points + Brainiest to the best answer :)
Answers
Answer/Step-by-step explanation:
Part A and B:
B to A 0.5 + -1.5 = -2 or I-2I Distance = 2
B to x 0.5 + 0 = 0.5 Distance = 0.5
x to A 0 + - 1.5 = -1.5 or I-1.5I Distance = 1.5
Find h as indicated in the figure. Round to the nearest foot.
Answers
By using trigonometric functions and law of sines, the length h indicated in the figure is approximately 87.997 feet.
What is the value of a length of a triangle within a geometric system?
In this system we find a picture of a geometric system formed by the two triangles, one of which with a right angle. We need to use trigonometric functions, law of sines and law of cosine to determine the missing length. First, use the law of sines:
(129 ft) / sin 33.7° = r / sin 26°
r = 129 ft × sin 26° / sin 33.7°
r ≈ 101.920 ft
Lastly, we find the value of the length h by trigonometric functions:
h = r · sin 59.7°
h = (101.920 ft) · sin 59.7°
h ≈ 87.997 ft
The length h indicated in the figure is approximately 87.997 feet.
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A group of friends wants to go to the amusement park. They have $116 to spend on parking and admission. Parking is $10.25, and tickets cost $35.25 per person, including tax. Which equation could be used to determine pp, the number of people who can go to the amusement park?
Answers
Answer:
2 people
Step-by-step explanation:
no. of people = x
total parking costs = 10.25x
total tickets cost = 35.25x
total = 10.25x + 35.25x
suppose 3 people go, then the total cost will be
10.25(3) + 35.25(3) = 136.5 and this is greater than 116
Suppose 2 people go then the cost will be
10.25(2) + 35.25(2) = 91 which is less than 116
so only 2 people can go.
Struggling, need help solving and a double check lolz
Answers
Answer:
Hello,
answer d
Step-by-step explanation:
I deduced yes.
So 3r+12=4r-2 ==> r=14
And m angle 1+m angle2=7r+10=7*14+10=108
answer d
i need help solving this problem
Answers
Answer:
[tex]3x^7{\cdot} (4x^{-5})^2=\dfrac{48}{x^3}[/tex]
Step-by-step explanation:
We need to simplify the given expression :
[tex]3x^7{\cdot} (4x^{-5})^2[/tex]
Use property : [tex]x^{-a}=\dfrac{1}{x^a}[/tex]
[tex]3x^7{\cdot} (\dfrac{4}{x^5})^2\\ =3x^7{\cdot} \dfrac{16}{x^{10}}\ \ [\because (x^a)^b=x^{a\times b}]\\\\=\dfrac{48}{x^3}[/tex]
So, the simplified form of the given expression is [tex]\dfrac{48}{x^3}[/tex]
If anyone could help me I would really appreciate it. Thank You
Answers
Answer:
with what?
Step-by-step explanation:
HELPPP I WILL BRAINLIST!!
Answers
Answer:
Step-by-step explanation:
8 (x -3) +7 = 2x (4 -17)
8(x -3) +7 = 2x (-13) here was the error because the had 13 that is incorrect
8x -24 +7 = -26x
8x -17 = -26x
-17 = -26x -8x
-17 = -34x
-17/-34 = x
1/2 =x
Please help asap!! I will mark you as brainliest :)
Answers
Answer:
It does slope= 5/4
Step-by-step explanation:
There is a slope
-2-3/ -3-1
-5/-4
5/4
Answer:
Yes, the line is proportional.
Step-by-step explanation:
As the graph is linear, when x increases, y will increase by an unchanging amount. In this case, when x increase by 1, y will always increase by 1.
ASAP can someone please help me
Answers
The price paid for a $250 table after a 30% discount is applied
Answers
Answer:
GAFD
Step-by-step explanation:
250*0.3 is 75
250-75 175
so D
GAFD
Hope this helps plz hit the crown :D
Answer:
GEFD
Step-by-step explanation:
What is the slope of the line through the points (2,5) and (6,13)?
A. 1/2
B. -2
C. 7/3
D. 2
Answers
Answer:
1/2
Step-by-step explanation:
What is the slope of the line in the graph?
4-
4 5
there is a picture ^
Answers
Answer: x+1 is the equation and the slope will be 1/1
Step-by-step explanation:
The doctor's office where you work needs to store 8 filing cabinets with patient information in one of three secure storage rooms. The filing cabinets need a total of 55 square feet of space. The doctor has asked you to identify which room the filing cabinets will fit
Answers
Answer:
Square B 9 × 7.5
Step-by-step explanation:
The computation is shown below:
9 × 7 = 63 > 55
8 × 5 = 40 < 55
5 × 10 = 50 < 55
As it can be seen that in only one condition the total of square feet is less and in the other conditions the total of square feet is more
Therefore the option Square B is correct
And, the rest of the options are incorrect
The same to be considered
How much more interest is earned on an investment of $12,585 at 3.5% interest over 5 years if the interest is compounded annually rather than earning simple interest? a. They are the same. b. $159.65 c. $2,362.03 d. $12,744.65
Answers
$159.65 is earned if compounded annually rather than simple interest.
The simple interest is calculated using the formula:
I = PRT I = 12,585 * 0.035* 5I = $2,202.375For the compound interest
A = P(1+r)^n
A = 12585(1+0.035)^5
A = 12585*1.18768
A =14,946.95
Compound interest = 14,946.95 -12585
Compound interest = $2,361.9528
Taking the difference in the interest = 2,361.9528 - 2,202.375
Difference = $159.65$159.65 is earned if compounded annually rather than simple interest.
Hence the $159.65 is earned if compounded annually rather than simple interest.
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Answer:
B
Step-by-step explanation:
Perry currently has $238 dollars and is spending $6 per day. Nick has no money but is earning $8 each day. After how many days will they have the same amount of money?
Answers
Answer:
are you sure it is not 180? if it is it is 12.87
but if it is 238 it is 21 days or something close
if i flip a coin 4 times what is the probability of getting at least 1 head
Answers
Answer:
at least 80%
Step-by-step explanation:
A cylindrical mailing tube has a length of 20 inches and diameter of 4 inches.
O
What is the approximate volume of the cylinder, to the nearest tenth of a cubic inch?
(Use 3.14 for pi.)
Answers
Answer:
Volume = 251.2 cubic inches
Step-by-step explanation:
You get the volume of a cylinder by multiplying the area of the base with the height.
Since the diameter is 4 inches, the radius of the base is 4/2 = 2 inches
So, volume = base area* height
= 2² * 3.14 * 20
= 251.2
The approximate volume of the cylinder mailling tube, to the nearest tenth of a cubic inch is 251.2 in³.
What is of volume of cylinder?Volume of cylinder is the amount of quantity, which is obtained by the solid or object in the 3 dimensional space.
Volume of cylinder is the can be given as,
[tex]V=\pi r^2h[/tex]
Here, (r) is the radius of the base of the cylinder and (h) is the height of the cylinder.
A cylindrical mailing tube has a length of 20 inches and diameter of 4 inches. The radius is half of the diameter of the cyilnder. Thus the radius of the cylinder is,
[tex]r=\dfrac{4}{2}\\r=2\rm\; in[/tex]
Put the value of radius and height of the cylinder in the above formula as,
[tex]V=3.14 (2)^2(20)\\V=251.2\rm\; in^3[/tex]
Thus, the approximate volume of the cylinder mailling tube, to the nearest tenth of a cubic inch is 251.2 in³.
(Use 3.14 for pi.)
Learn more about the volume of cylinder here;
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There are 2.54 cm in 1 inch. they are 100 cm in 1 m, to the nearest meter, how many meters are in 474 inches
Answers
Multiply total meters by 100 to get total centimeters:
6 meters x 100 = 600 centimeters.
Now divide total centimeters by 2.554 to get total inches:
600 centimeters / 2.54 = 236.22 inches.
Rounded to the nearest inch = 236 inches.
Let f (x) = -5x + 4. Write a function g whose graph is a reflection in the y-axis of the graph of f.
Answers
If the function is reflected across the yaxis of the graph of f, the resulting function will be g(x) = 5x + 4
Translation of functionsTranslation is the technique that is used to change the position of a figure on an xy-plane.
For instance, if the function f(x) is reflected in the y-axis, the resulting function will be g(x) = -f(x)
Given the function f(x)=|x|-3, if the function is reflected in the y-axis of the graph of f.f, the resulting function will be;
g(x) = f(-x)
g(x) = (-5x) + 4)
g(x) = 5x + 4
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If f(5) = a , what is the value of a?
Answers
Answer:A=5F
Step-by-step explanation: Flip the equation.
what is the least common multiple for 5 and 24
Answers
Answer:
120
Step-by-step explanation:
Since they don't have any common factors, we have to multiply them.
24 x 5 = 120
I hope you understood what I wrote :)
EASY POINT FOR Y'ALL
Answers
Answer:
A
Step-by-step explanation:
its A
when somethinng is imput, the output can only be 1 answer
the rest have an imput with two different outputs
take care
NEED ANSWER ASAP!!!!!!!!!
An airplane is flying at 32,000 feet when it starts it’s decent. It is
descending at a rate of 2000 feet per minute. Let x represent the minutes
of the flights descent and y represent the plane’s altitude.
a. Fill in the table.
b. Write an equation in slope-intercept form for the plane’s altitude.
c. Graph the equation from part (b).
Answers
Answer:
10,000
Step-by-step explanation:
f = feet above ground
r = rate of descent
m = minutes
f = 30000 - r · m
f = 30000 - 20000m
After five minutes:
f = 30000 - 2000(5)
f = 30000 - 10000
f = 20000
After five minutes the plane is at 10,000. feet.
A box is filled with 6 blue cards, 6 brown cards, and 3 green cards. A card is chosen at random from the box. What is the probability that it is a blue or a green card?
Answers
Answer:
60% chance of a blue or green card
*The sum of 5
and the twice a
number is at
most 27*
Answers
Answer:
Well i think that is true. and the mystery number i believe is 11
Step-by-step explanation:
Well, first subtract 5 from 27, you get 22. Then divide that by two (because that is half). And you get 11.
11 · 11 = 22
22 + 5 = 27
Really hope this helps!
Answer:
x [tex]\leq[/tex] 11
Step-by-step explanation:
The phrase "at most" is telling us that we have an inequality where the answer will be less than or equal to 27. If we let x be our missing number:
2x + 5 [tex]\leq[/tex] 27
2x [tex]\leq[/tex] 22
x [tex]\leq[/tex] 11
Match each slope with the correct line.
3
2/4
2/3
Need help asap!!